Having spent the last post whining about my troubles with the "two-socks-at-once" concept, I was inspired to think about what was causing these problems. And - why didn't I do this earlier? - a little thought was able to solve several of the biggies.
1) Every time you flip the needles over, check which way both free ends of yarn are going before you start to knit. This mostly takes care of the "why is my yarn wrapped around the needles twice?" problem. If you alternate which way you flip the needles over, you can also solve a lot of the "tangled yarn" problems.
2) Before you start to knit, tug gently on the needles you're holding. You should feel tension. If you don't, you aren't holding ends that belong to the same needles. Correct this.
3) It turns out that you don't have to remove one sock to knit the other heel.
4) Laddering is hidden much better if you place it along one of the knit-purl interchanges.
Now I'm past both heels, and cruising up the leg!